Black Flag's lead writer actually commented on a question similar to this at Comic Con 2013. He said in their research, they found that the crews on those of a Spanish or British vessel wouldn't actually wear any official uniforms, only the officers would. The crews themselves dressed like Kenway's crew. Of course this led to everyone looking the same during boarding and confusion for the player, so they gave the entire crew officer uniforms. I can't really comment on if the color and look of the uniforms are historically correct though.

It's a big assumption that Assassin's Creed 4: Black Flag actually tried to get the material culture of that era correct. They didn't. If you want to know what parts of the Pirate story they got right and wrong, see my review here.

As for uniform color - white is what I've read before. The Spanish maritime forces of the era had white and some blue for the soldiers they put aboard their ships (Spain still had a strong separation between sailor and soldiers on their ships at the time, putting soldiers onboard to take care of most of the fighting rather than the sailors - they hadn't done the thing of having sailors do most of the fighting and regulating soldiers to a smaller numbers and into what the "marines" were on other ships). You can see a historian's researched depictions of them in Historia de los Uniformes de la Armada Española (1717 - 1814). Here are two images: image 1 image 2